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Advanced topics in applied mathemati...

Nair, Sudhakar, (1944-)

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Advanced topics in applied mathematics : = for engineering and the physical sciences /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Advanced topics in applied mathematics :/ Sudhakar Nair.
其他題名:	for engineering and the physical sciences /
作者:	Nair, Sudhakar,
出版者:	New York :Cambridge University Press, : c2011.,
面頁冊數:	x, 222 pages :illustrations ;24 cm.
標題:	Differential equations. -
ISBN:	9781107006201 (hbk.) :

Advanced topics in applied mathematics : = for engineering and the physical sciences /
Nair, Sudhakar,1944-

Advanced topics in applied mathematics :for engineering and the physical sciences /Sudhakar Nair. - New York :Cambridge University Press,c2011. - x, 222 pages :illustrations ;24 cm.

Includes bibliographical references and indexes.

Green's Functions --Machine generated contents note:

"This book is ideal for engineering, physical science, and applied mathematics students and professionals who want to enhance their mathematical knowledge. Advanced Topics in Applied Mathematics covers four essential applied mathematics topics: Green's functions, Integral equations, Fourier transforms, and Laplace transforms. Also included is a useful discussion of topics such as the Wiener-Hopf method, Finite Hilbert transforms, Cagniard-De Hoop method, and the proper orthogonal decomposition. This book reflects Sudhakar Nair's long classroom experience and includes numerous examples of differential and integral equations from engineering and physics to illustrate the solution procedures. The text includes exercise sets at the end of each chapter and a solutions manual, which is available for instructors"--

ISBN: 9781107006201 (hbk.) :US85.00

LCCN: 2010052380Subjects--Topical Terms:

517952
Differential equations.

LC Class. No.: TA347.D45 / N35 2011

Dewey Class. No.: 620.001/51

Advanced topics in applied mathematics : = for engineering and the physical sciences /
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020 $a 9781107006201 (hbk.) : $c US85.00
020 $a 1107006201 (hbk.)
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035 $a (OCoLC)690090214
035 $a PS-BW-100-N-06
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050 0 0 $a TA347.D45 $b N35 2011
082 0 0 $a 620.001/51 $2 22
100 1 $a Nair, Sudhakar, $d 1944- $e author. $3 1314307
245 1 0 $a Advanced topics in applied mathematics : $b for engineering and the physical sciences / $c Sudhakar Nair.
260 # $a New York : $b Cambridge University Press, $c c2011.
300 $a x, 222 pages : $b illustrations ; $c 24 cm.
336 $a text $2 rdacontent
337 $a unmediated $2 rdamedia
338 $a volume $2 rdacarrier
504 $a Includes bibliographical references and indexes.
505 0 0 $g Machine generated contents note: $g 1. $t Green's Functions -- $g 1.1. $t Heaviside Step Function -- $g 1.2. $t Dirac Delta Function -- $g 1.2.1. $t Macaulay Brackets -- $g 1.2.2. $t Higher Dimensions -- $g 1.2.3. $t Test Functions, Linear Functionals, and Distributions -- $g 1.2.4. $t Examples: Delta Function -- $g 1.3. $t Linear Differential Operators -- $g 1.3.1. $t Example: Boundary Conditions -- $g 1.4. $t Inner Product and Norm -- $g 1.5. $t Green's Operator and Green's Function -- $g 1.5.1. $t Examples: Direct Integrations -- $g 1.6. $t Adjoint Operators -- $g 1.6.1. $t Example: Adjoint Operator -- $g 1.7. $t Green's Function and Adjoint Green's Function -- $g 1.8. $t Green's Function for L -- $g 1.9. $t Sturm-Liouville Operator -- $g 1.9.1. $t Method of Variable Constants -- $g 1.9.2. $t Example: Self-Adjoint Problem -- $g 1.9.3. $t Example: Non-Self-Adjoint Problem -- $g 1.10. $t Eigenfunctions and Green's Function -- $g 1.10.1. $t Example: Eigenfunctions -- $g 1.11. $t Higher-Dimensional Operators -- $g 1.11.1. $t Example: Steady-State Heat Conduction in a Plate -- $g 1.11.2. $t Example: Poisson's Equation in a Rectangle
505 0 0 $g 1.11.3. $t Steady-State Waves and the Helmholtz Equation -- $g 1.12. $t Method of Images -- $g 1.13. $t Complex Variables and the Laplace Equation -- $g 1.13.1. $t Nonhomogeneous Boundary Conditions -- $g 1.13.2. $t Example: Laplace Equation in a Semi-infinite Region -- $g 1.13.3. $t Example: Laplace Equation in a Unit Circle -- $g 1.14. $t Generalized Green's Function -- $g 1.14.1. $t Examples: Generalized Green's Functions -- $g 1.14.2. $t A Recipe for Generalized Green's Function -- $g 1.15. $t Non-Self-Adjoint Operator -- $g 1.16. $t More on Green's Functions -- $g 2. $t Integral Equations -- $g 2.1. $t Classification -- $g 2.2. $t Integral Equation from Differential Equations -- $g 2.3. $t Example: Converting Differential Equation -- $g 2.4. $t Separable Kernel -- $g 2.5. $t Eigenvalue Problem -- $g 2.5.1. $t Example: Eigenvalues -- $g 2.5.2. $t Nonhomogeneous Equation with a Parameter -- $g 2.6. $t Hilbert-Schmidt Theory -- $g 2.7. $t Iterations, Neumann Series, and Resolvent Kernel -- $g 2.7.1. $t Example: Neumann Series -- $g 2.7.2. $t Example: Direct Calculation of the Resolvent Kernel -- $g 2.8. $t Quadratic Forms -- $g 2.9. $t Expansion Theorems for Symmetric Kernels
505 0 0 $g 2.10. $t Eigenfunctions by Iteration -- $g 2.11. $t Bound Relations -- $g 2.12. $t Approximate Solution -- $g 2.12.1. $t Approximate Kernel -- $g 2.12.2. $t Approximate Solution -- $g 2.12.3. $t Numerical Solution -- $g 2.13. $t Volterra Equation -- $g 2.13.1. $t Example: Volterra Equation -- $g 2.14. $t Equations of the First Kind -- $g 2.15. $t Dual Integral Equations -- $g 2.16. $t Singular Integral Equations -- $g 2.16.1. $t Examples: Singular Equations -- $g 2.17. $t Abel Integral Equation -- $g 2.18. $t Boundary Element Method -- $g 2.18.1. $t Example: Laplace Operator -- $g 2.19. $t Proper Orthogonal Decomposition -- $g 3. $t Fourier Transforms -- $g 3.1. $t Fourier Series -- $g 3.2. $t Fourier Transform -- $g 3.2.2. $t Riemann-Lebesgue Lemma -- $g 3.2.2. $t Localization Lemma -- $g 3.3. $t Fourier Integral Theorem -- $g 3.4. $t Fourier Cosine and Sine Transforms -- $g 3.5. $t Properties of Fourier Transforms -- $g 3.5.1. $t Derivatives of F -- $g 3.5.2. $t Scaling -- $g 3.5.3. $t Phase Change -- $g 3.5.4. $t Shift -- $g 3.5.5. $t Derivatives of � -- $g 3.6. $t Properties of Trigonometric Transforms -- $g 3.6.1. $t Derivatives of Fc and Fs -- $g 3.6.2. $t Scaling -- $g 3.6.3. $t Derivatives of �
505 0 0 $g 4.2. $t Properties of the Laplace Transform -- $g 4.2.1. $t Linearity -- $g 4.2.2. $t Scaling -- $g 4.2.3. $t Shifting -- $g 4.2.4. $t Phase Factor -- $g 4.2.5. $t Derivative -- $g 4.2.6. $t Integral -- $g 4.2.7. $t Power Factors -- $g 4.3. $t Transforms of Elementary Functions -- $g 4.4. $t Convolution Integral -- $g 4.5. $t Inversion Using Elementary Properties -- $g 4.6. $t Inversion Using the Residue Theorem -- $g 4.7. $t Inversion Requiring Branch Cuts -- $g 4.8. $t Theorems of Tauber -- $g 4.8.1. $t Behavior of �(t) as t ��0 -- $g 4.8.2. $t Behavior of �(t) as t ��-- $g 4.9. $t Applications of Laplace Transform -- $g 4.9.1. $t Ordinary Differential Equations -- $g 4.9.2. $t Boundary Value Problems -- $g 4.9.3. $t Partial Differential Equations -- $g 4.9.4. $t Integral Equations -- $g 4.9.5. $t Cagniard-De Hoop Method -- $g 4.10. $t Sequences and the Z-Transform -- $g 4.10.1. $t Difference Equations -- $g 4.10.2. $t First-Order Difference Equation -- $g 4.10.3. $t Second-Order Difference Equation -- $g 4.10.4. $t Brilluoin Approximation for Crystal Acoustics.
520 # $a "This book is ideal for engineering, physical science, and applied mathematics students and professionals who want to enhance their mathematical knowledge. Advanced Topics in Applied Mathematics covers four essential applied mathematics topics: Green's functions, Integral equations, Fourier transforms, and Laplace transforms. Also included is a useful discussion of topics such as the Wiener-Hopf method, Finite Hilbert transforms, Cagniard-De Hoop method, and the proper orthogonal decomposition. This book reflects Sudhakar Nair's long classroom experience and includes numerous examples of differential and integral equations from engineering and physics to illustrate the solution procedures. The text includes exercise sets at the end of each chapter and a solutions manual, which is available for instructors"-- $c Provided by publisher.
650 # 0 $a Differential equations. $3 517952
650 # 0 $a Engineering mathematics. $3 516847
650 # 0 $a Mathematical physics. $3 516853